Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems

We consider quantum unbounded spin systems (lattice boson systems) in -dimensional lattice space Z. Under appropriate conditions on the interactions we prove that in a region of high temperatures the Gibbs state is unique, is translationally invariant, and has clustering properties. The main methods we use are the Wiener integral representation, the cluster expansions for zero boundary conditions and for general Gibbs state, and explicitly -dependent probability estimates. For one-dimensional systems we show the uniqueness of Gibbs states for any value of temperature by using the method of perturbed states. We also consider classical unbounded spin systems. We derive necessary estimates so that all of the results for the quantum systems hold for the classical systems by straightforward applications of the methods used in the quantum case.     

Gibbs states of the Hopfield model with extensively many patterns

We consider the Hopfield model withM(N)=N patterns, whereN is the number of neurons. We show that if is sufficiently small and the temperature sufficiently low, then there exist disjoint Gibbs states for each of the stored patterns, almost surely with respect to the distribution of the random patterns. This solves a provlem left open in previous work. The key new ingredient is a self-averaging result on the free energy functional. This result has considerable additional interest and some consequences are discussed. A similar result for the free energy of the Sherrington-Kirkpatrick model is also given.     

X-ray emission spectroscopy with EPMA applied to high Tc Superconductors using new spectrometer crystals

The High Temperature Superconductors are characterized by a very anisotropical structure and by typical arrangements of Cu- and O-atoms within CuO₂-planes. In studying the electronic structure of these compounds there is a strong demand for high resolution valence band spectroscopy. Using an electron probe microanalyzer we study the X-ray emission of O-K_ga and Cu-L emerging from polycrystalline YBa₂Cu₃O₇ and Tl₂Ba₂Ca₂Cu₃O₁₀. The O-K emission band is analyzed using a chlinochlore crystal in (001) orientation (2d = 28.4 Å). For the Cu-L emission band we use a beryl crystal in (10¯10) orientation (2d = 15.9 Å). Furthermore, orientation dependent X-ray emission spectroscopy of single-crystalline YBa₂Cu₃O₇ and Tl₂Ba₂Ca₁Cu₂O₈ specimens was performed. We present the partial O-K spectra which represent the O-2p ( = x, y, z) electronic densities of states of the valence band and compare them with calculated data.     

On some variational approximations in two-dimensional classical lattice systems

A new derivation is presented of some variational approximations for classical lattice systems that belong to the class of cluster-variation methods, among them the well-known Bethe-Peierls and Kramers-Wannier approximations. The limiting behavior of a hierarchical sequence of cluster-variation approximations, the so-calledC hierarchy, is discussed. It is shown that this hierarchy provides a monotonically decreasing sequence of upper boundsf _n on the free energy per lattice sitef and thatf _n f asn . Our results are based on extension theorems for states given on subsets of the lattice, which might be of some independent interest, and on an application of transfer matrix concepts to the variational characterization of translation-invariant equilibrium states.     

PHOTOEMISSION WITHIN AND BEYOND THE ONE-STEP MODEL

Photoemission in the vacuum ultraviolet photon regime has proved to be an effective tool for the investigation of valence band surface electronic structure. The interpretation cannot be exclusively confined to the valence bands but has to consider cross sections with realistic final states consistently designed within the one-step model. Therefore especially in the surface sensitive photoemission, several effects hide the final goal of deducing the energetic and wavefunction structure together with microscopic potential parameters through a convincing agreement of calculated with measured spectra. The final states band structure is much less well understood than the valence band structure under consideration. The optical potential, which controls the surface sensitivity through the underlying damping mechanisms, widely relies on empirical assumptions. Furthermore, the photon field is not only strongly influenced but in the vicinity of the plasma frequency also deteriorated by the electronic response. In view of high resolution spectroscopy the accuracy of the data interpretation is affected, and in fact, band-mapping methods are no longer valid. Examples of recent calculations to account for these effects are reviewed.     

Triplet states of humic acids studied by laser flash photolysis using different excitation wavelengths

The spectra and kinetics of short-lived intermediates formed from aqueous (0.1 N NaOH) solutions of the natural mixture of humic and fulvic acids (HFA) were studied by laser flash photolysis using excitation wavelengths of 337, 390, 470, and 520 nm. Laser photolysis of HFA with light of 520 and 470 nm results in the formation of triplet excited states (T_HFA) characterized by the broad absorption spectrum with a maximum near 630 nm and lifetimes of 0.15 ms in deoxygenated solutions. The formation of two types of T_HFA with lifetimes of 0.1 and 2 ms and absorption spectra with maxima at 570 nm is observed under photolysis with light of 337 and 390 nm. The estimation of quantum yields of T_HFA gives 1 and 0.3% under photolysis with excitation wavelengths of 337 and 520 nm, respectively. The rate constants of T_HFA quenching by molecular oxygen are equal to (7—8)·10⁸ L mol^–1 s^–1.     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for iterative evaluation of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.     

Binding site optimisation for artificial enzymes by diffusion NMR of small molecules

A binding site optimisation protocol for the design of artificial enzymes based on "small molecule-small molecule" binding studies by diffusion NMR is presented. Since the reaction chosen was the hydrolysis of ester 1 ([4-(4-carboxy-1-oxobutyl)-aminobenzyl]-phenethyl ester), an analogous phosphonate ester 2 ([4-(4-carboxy-1-oxobutyl)-aminobenzyl]-phosphonic phenethyl ester) was selected as a suitable transition state analogue (TSA). The key objective of the NMR studies was to find a unit with functional groups capable of binding to the acidic sites of the TSA. Nine dipeptides, mainly with basic and hydroxyl groups, were used and their affinity to the TSA was studied by measuring the change in the diffusion coefficient, D(pep), upon binding by pulse field gradient NMR. The value of D(pep) at 298 K in D(2)O at pD 5, 7 and 10 was measured both in free solution, and mixtures containing one dipeptide and the TSA. As both components are low molecular weight species with M < 500, a TSA-to-dipeptide ratio of 10:1 was used to detect significant changes in D(pep). The results revealed that dipeptides with basic residues show higher affinity to the TSA than those with hydroxyl or aliphatic side chains in aqueous solutions. The dipeptide showing the most significant relative change in D(pep) was H-Arg-Arg-OH, and the binding constant was estimated to be 86 L M(-1) by measuring D(pep) at varying concentrations of the TSA. In addition, binding of the TSA to a new water-soluble polymer with a polyallylamine backbone and randomly distributed Arg-Arg binding sites was examined, and the binding constant was estimated to be > or =1500 L M(-1). As confirmed by further catalytic activity tests, polymers containing Arg-Arg as a binding site are capable of significant rate accelerations in the hydrolysis of ester 1.     

Effect of the coordination sphere of d<Superscript>0</Superscript> metallocene on triplet-triplet energy transfer

The triplet nature of rare long-lived states of d⁰ metallocenes formed upon ligand-to-metal energy transfer was confirmed by studies of triplet-triplet charge transfer in biscyclopentadienyl complexes Cp₂MCl₂ (M = Zr (1), Hf (2)). The interaction between precatalysts and substrates of catalytic polymerization systems, viz., complexes 1 and 2 and unsaturated hydrocarbons (alkenes and dienes), was studied in the region of concentrations close to catalytic values. For organometallic π-complexes, it has been shown for the first time that, in the case of the unsaturated hydrocarbons, the efficiency of energy transfer obeys the Perrin equation. The process occurs at distances R ₀ close to the diameter of the interacting molecules and is well described by the exchange-resonant mechanism of interaction. In the case of the cyclopentadiene-Cp₂MCl₂ (M = Zr, Hf) systems, R ₀ = 14.6 Å. A linear relationship between the critical radius of the quenching sphere R ₀ and the number of carbon atoms in a linear α-olefin has been revealed for the first time and evidences the formation of a π-complex between the precatalyst and substrate molecules. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 35–39, January, 2007.     

Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.